Europe's economic outlook, jihadist attacks, the refugee and migrant drama, the Syrian conflict, and relations with Russia and Turkey will all be on the table on the lush Italian island of Ventotene.
But more than anything else, the meeting, held three weeks before an informal EU summit in Bratislava of 27 states - minus Britain - will focus on how to reverse the rise of euroscepticism and strengthen the hard-hit bloc.
It will be the second round of trilateral talks between Italian Prime Minister Matteo Renzi, French President Francois Hollande and German Chancellor Angela Merkel. At their first, shortly after Britain's June 23rd vote, the leaders called for "a new impulse" for the EU.
Critics have demanded less talk more action over a crisis some states fear could lead to similar referendums in other countries, particularly the Netherlands, which opposes changes to the EU to achieve closer integration.
Coming up with a road map acceptable to all will not be easy, with the Czech Republic, Hungary, Poland and Slovakia vowing after Britain's vote to draw up their own plans for a less-centralised EU.
Renzi will welcome Hollande and Merkel in Naples at 1400 GMT before they travel on to Ventotene, where they will visit the grave of Altiero Spinelli, one of the founding fathers of the ideal of European integration.
Imprisoned on the island by the fascist government during the Second World War, Spinelli and fellow captive Ernesto Rossi co-wrote the "Ventotene manifesto" calling for a federation of European states.
Defence, economy, culture
In another symbolic move, the leaders will hold a working dinner and press conference on Italy's Garibaldi aircraft carrier, the flagship of the EU's "Sophia" mission against people trafficking in the Mediterranean.
It will be the start of an intensive tour of talks for the German chancellor as she attempts to coordinate a response to one of the EU's biggest crises in decades and quell fears Berlin wants to monopolise the debate.
After a series of deadly attacks by the Islamic State group (IS), the three leaders are expected to explore greater co-operation on counter-terrorism and an integrated European security and defence policy -- a long-cherished objective that could be easier to achieve now sceptical Britain has departed.
Italy's defence and foreign affairs ministers have proposed creating "a Schengen-like defence agreement to respond to terrorism", with a "multinational force" under a single command for specific missions.
It is an idea France is keen on, but Germany is unlikely to get behind Paris's suggestion for it to be funded with eurobonds, a move Berlin fears would leave it vulnerable to the debt burdens of eurozone peers.
In terms of the economy, Hollande wants the Juncker Plan - the EU's investment fund for infrastructure, education, research and innovation - to be doubled, according to a French diplomatic source.
Renzi is tipped to unveil a proposal to use part of those funds to restore European cultural monuments.
But while Hollande and Renzi want to tackle Europe's identity crisis through investments, Merkel is unlikely to be moved by their anti-austerity overtures.
All three leaders have been hit in the polls by varying toxic combinations of refugee crisis, economic slump and terror attacks, with eurosceptic or populist parties gaining ground.
And with 2017 bringing a general election in Germany and presidential election in France, they will be wary of ignoring opposition to further European integration at home, leaving them little room for manoeuvre.